Q. The trapezoidal rule for integration give exact result when the integrand is a polynomial of degree:

View solution

Q. The minimum number of colours required to colour the vertices of a cycle with n nodes in such a way that no two adjacent nodes have the same colour is

View solution

Q. If X, then Y unless Z" is represented by which of the following formulae in propositional logic? ("¬" is negation "^" is conjunction, and "→" is implication)

View solution

Q. The decimal value 0.25

View solution

Q. Maximum number of edges in a n - node undirected graph without self loops is

View solution

Q. The Newton-Raphson iteration Xn + 1 = (Xn/2) + 3/(2Xn) can be used to solve the equation

View solution

Q. Four fair coins are tossed simultaneously. The probability that at least one head and one tail turn up is :

View solution

Q. A B+ -tree index is to be built on the Name attribute of the relation STUDENT. Assume that all student names are of length 8 bytes, disk block are size 512 bytes, and index pointers are of size 4 bytes. Given this scenario, what would be the best choice of the degree (i.e. the number of pointers per node) of the B+ -tree?

View solution

Q. Let P(E) denote the probability of the event E. Given P(A) = 1, P(B) = 1/2, the values of P(A | B) and P(B | A) respectively are

View solution

Q. Let A be a sequence of 8 distinct integers sorted in ascending order. How many distinct pairs of sequences, B and C are there such that (i) each is sorted in ascending order, (ii) B has 5 and C has 3 elements, and (iii) the result of merging B and C gives A?

View solution

Q. Let G be an arbitrary graph with n nodes and k components. If a vertex is removed from G, the number of components in the resultant graph must necessarily lie between

View solution

Q. Let f : A → B be an injective (one-to-one) function.

Define g : 2^A → 2^B as :
g(C) = {f(x) | x ∈ C}, for all subsets C of A.
Define h : 2^B → 2^A as :
h(D) = {x | x ∈ A, f(x) ∈ D}, for all subsets D of B.

Which of the following statements is always true ?

View solution

Q. Consider the set {a, b, c} with binary operators + and × defined as follows :

+ a b c × a b c
a b a c a a b c
b a b c b b c a
c a c b c c c b

For example, a + c = c, c + a = a, c × b = c and b × c = a. Given the following set of equations :

(a × x) + (a × y) = c
(b × x) + (c × y) = c

The number of solution(s) (i.e., pair(s) (x, y)) that satisfy the equations is :

View solution

Q. Consider two languages L1 and L2 each on the alphabet ∑. Let f : ∑ → ∑ be a polynomial time computable bijection such that (∀ x) [x ∈ L1 iff f(x) ∈ L2]. Further, let f^-1 be also polynomial time computable. Which of the following CANNOT be true?

View solution

Q. In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. If all permutations are equally likely, what is the expected number of inversions in a randomly chosen permutation of 1.....n ?

View solution

Q. In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst case time complexity of the Insertion Sort algorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?

View solution

Q. The cube root of a natural number n is defined as the largest natural number m such that m^3 ≤ n. The complexity of computing the cube root of n (n is represented in binary notation) is:

View solution

Q. The following resolution rule is used in logic programming:

Derive clause (P v Q) from clauses (P v R), (Q v ¬ R)

Which of the following statements related to this rule is FALSE?

View solution

Q. Identify the correct translation into logical notation of the following assertion.

"Some boys in the class are taller than all the girls"

Note : taller(x,y) is true if x is taller than y.

View solution

Q. If a fair coin is tossed four times. What is the probability that two heads and two tails will result?

View solution